Advertisements
Advertisements
प्रश्न
Simplify:
`((a^(x + y))^(x - y)(a^(y - z))^(y + z))/((a^(x + z))^(x - z))`
सोपे रूप द्या
Advertisements
उत्तर
Given expression:
`((a^(x + y))^(x - y)(a^(y - z))^(y + z))/((a^(x + z))^(x - z))`
Step-wise calculation:
1. Apply the power of a power rule (am)n = amn:
`(a^((x + y)(x - y)) xx a^((y - z)(y + z)))/(a^((x + z)(x - z))`
2. Use the difference of squares formula (m + n)(m – n) = m2 – n2:
`(a^(x^2 - y^2) xx a^(y^2 - z^2))/(a^(x^2 - z^2))`
3. Multiply terms in numerator with the same base by adding exponents:
`(a^(x^2 - y^2 + y^2 - z^2))/(a^(x^2 - z^2)) = (a^(x^2 - z^2))/(a^(x^2 - z^2))`
4. Simplify by subtracting exponents in the numerator and denominator:
`a^((x^2 - z^2) - (x^2 - z^2)) = a^0`
`a^((x^2 - z^2) - (x^2 - z^2)) = 1`
The given expression simplifies to 1.
shaalaa.com
या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
