Question

Simplify the expression using the properties of exponents. Expand any numerical portion of your answer and only include positive exponents.

(2x^2y^−2)^−3(7x^−1y)^−1

Answer 1

To simplify the expression, let's start by applying the negative exponent property.

Recall that for any non-zero number a and positive integer n, (a^m)^n = a^(m*n). Using this property:

(2x^2y^−2)^−3(7x^−1y)^−1
= (2^(-3)x^(2*(-3))y^((-2)*(-3)))(7^(-1)x^((-1)*(-1))y^(-1))
= 2^(-3)x^(-6)y^6 * 7^(-1)x^1 * y^(-1)

Next, simplify the numerical portion by expanding the negative exponents:

2^(-3) = 1/2^3 = 1/8
7^(-1) = 1/7

Now, let's simplify the expression further by combining the x and y terms:

(1/8)(1/x^6)(y^6)(1/7)(x)(1/y)
= 1/(8x^6y)(7x)
= 1/(56x^7y)

Therefore, the simplified expression is 1/(56x^7y).