R.D. Sharma solutions for Mathematics [English] Class 8 chapter 2 - Powers [Latest edition]

Express the following as a rational number of the form \[\frac{p}{q},\] where p and q are integers and q ≠ 0.

Express the following as a rational number of the form \[\frac{p}{q},\] where p and q are integers and q ≠ 0. (−4)⁻²

Express the following as a rational number of the form \[\frac{p}{q},\] where p and q are integers and q ≠ 0.

Express the following as a rational number of the form \[\frac{p}{q},\] where p and q are integers and q ≠ 0.

Express the following as a rational number of the form \[\frac{p}{q},\] where p and q are integers and q ≠ 0.

Find the value of the following:
 3⁻¹ + 4⁻¹

Find the value of the following:
(3⁰ + 4⁻¹) × 2²

Find the value of the following:
(3⁻¹ + 4⁻¹ + 5⁻¹)⁰

Find the value of the following:
\[\left\{ \left( \frac{1}{3} \right)^{- 1} - \left( \frac{1}{4} \right)^{- 1} \right\}^{- 1}\]

Find the value of the following:

\[\left( \frac{1}{2} \right)^{- 1} + \left( \frac{1}{3} \right)^{- 1} + \left( \frac{1}{4} \right)^{- 1}\]

Find the value of the following:

Find the value of the following:

Find the value of the following:

Simplify:

Simplify:

Simplify:

Simplify:
\[\left( 3^{- 1} \times 4^{- 1} \right)^{- 1} \times 5^{- 1}\]

Simplify:

Simplify:

Simplify:

Simplify:

By what number should \[\left( \frac{1}{2} \right)^{- 1}\] be multiplied so that the product may be equal to \[\left( - \frac{4}{7} \right)^{- 1} ?\]

Write the following in exponential form:

Write the following in exponential form:

\[\left( \frac{2}{5} \right)^{- 2} \times \left( \frac{2}{5} \right)^{- 2} \times \left( \frac{2}{5} \right)^{- 2}\]

Evaluate:
5⁻²

Evaluate:
(−3)⁻²

Evaluate:
\[\left( \frac{1}{3} \right)^{- 4}\]

Evaluate:
\[\left( \frac{- 1}{2} \right)^{- 1}\]

Express the following as a rational number in the form \[\frac{p}{q}:\]

6⁻¹

Express the following as a rational number in the form \[\frac{p}{q}:\]

(−7)⁻¹

Express the following as a rational number in the form \[\frac{p}{q}:\]

Express the following as a rational number in the form \[\frac{p}{q}:\]

Express the following as a rational number in the form \[\frac{p}{q}:\]

Simplify:
\[\left\{ 4^{- 1} \times 3^{- 1} \right\}^2\]

Simplify:
\[\left\{ 5^{- 1} \div 6^{- 1} \right\}^3\]

Simplify:

Simplify:

\[\left\{ 3^{- 1} \times 4^{- 1} \right\}^{- 1} \times 5^{- 1}\]

Simplify:

\[\left( 4^{- 1} - 5^{- 1} \right) \div 3^{- 1}\]

Express the following rational numbers with a negative exponent:

Express the following rational numbers with a negative exponent:

Express the following rational numbers with a negative exponent:

Express the following rational numbers with a negative exponent:

Express the following rational numbers with a negative exponent:

Express the following rational numbers with a positive exponent:

Express the following rational numbers with a positive exponent:

Express the following rational numbers with a positive exponent:

Express the following rational numbers with a positive exponent:

Express the following rational numbers with a positive exponent:

Simplify:

Simplify:

Simplify:

Simplify:

Simplify:

By what number should \[\left( \frac{1}{2} \right)^{- 1}\] be multiplied so that the product may be equal to \[\left( \frac{- 4}{7} \right)^{- 1} ?\]

By what number should \[\left( \frac{5}{3} \right)^{- 2}\] be multiplied so that the product may be \[\left( \frac{7}{3} \right)^{- 1} ?\]

Find x, if \[\left( \frac{1}{4} \right)^{- 4} \times \left( \frac{1}{4} \right)^{- 8} = \left( \frac{1}{4} \right)^{- 4x}\]

Find x, if
\[\left( \frac{- 1}{2} \right)^{- 19} \times \left( \frac{- 1}{2} \right)^8 = \left( \frac{- 1}{2} \right)^{- 2x + 1}\]

Find x, if

Find x, if

Find x, if

Find x, if

if \[x = \left( \frac{3}{2} \right)^2 \times \left( \frac{2}{3} \right)^{- 4}\], find the value of x⁻².

If \[x = \left( \frac{4}{5} \right)^{- 2} \div \left( \frac{1}{4} \right)^2\], find the value of x⁻¹.

Find the value of x for which 5^2x ÷ 5⁻³ = 5⁵.

Express the following numbers in standard form:
6020000000000000

Express the following numbers in standard form:
0.00000000000943

Express the following numbers in standard form:
0.00000000085

Express the following numbers in standard form:
846 × 10⁷

Express the following numbers in standard form:
3759 × 10⁻⁴

Express the following numbers in standard form:
0.00072984

Express the following numbers in standard form:
0.000437 × 10⁴

Express the following numbers in standard form:
4 ÷ 100000

Write the following numbers in the usual form:
4.83 × 10⁷

Write the following numbers in the usual form:
3.02 × 10⁻⁶

Write the following numbers in the usual form:
4.5 × 10⁴

Write the following numbers in the usual form:
3 × 10⁻⁸

Write the following numbers in the usual form:
1.0001 × 10⁹

Write the following numbers in the usual form:
5.8 × 10²

Write the following numbers in the usual form:
3.61492 × 10⁶

Write the following numbers in the usual form:
3.25 × 10⁻⁷

Square of \[\left( \frac{- 2}{3} \right)\] is

Cube of \[\frac{- 1}{2}\] is

Which of the following is not equal to \[\left( \frac{- 3}{5} \right)^4 ?\]

Which  of the following is not reciprocal of \[\left( \frac{2}{3} \right)^4 ?\]

Which of the following numbers is not equal to \[\frac{- 8}{27}?\]
(a) \[\left( \frac{2}{3} \right)^{- 3}\]

(b) \[- \left( \frac{2}{3} \right)^3\]

(c) \[\left( - \frac{2}{3} \right)^3\]

(d) \[\left( \frac{- 2}{3} \right) \times \left( \frac{- 2}{3} \right) \times \left( \frac{- 2}{3} \right)\]

\[\left( \frac{3}{4} \right)^5 \div \left( \frac{5}{3} \right)^5\] is equal to

For any two non-zero rational numbers a and b, a⁴ ÷ b⁴ is equal to

For any two rational numbers a and b, a⁵ × b⁵ is equal to 

For a non-zero rational number a, a⁷ ÷ a¹² is equal to

For a non zero rational number a, (a³)⁻² is equal to