Algebra

x^7 * (y^2 * z^-7)^2 / (x^-6 * y^-1 * z^-8)

Step-by-step solution with explanation

Final Answer

Step-by-step solution

1

Expand the power inside parentheses

When you raise a product to a power, multiply each exponent by that power. Here we multiply each exponent inside the parentheses by 2.
2

Rewrite the full expression

Replace the parenthetical group with the expanded form. Now we have a straightforward division of terms with exponents.
3

Divide x terms using exponent rule

When dividing like bases, subtract the denominator's exponent from the numerator's exponent. Subtracting a negative becomes addition.
4

Divide y terms using exponent rule

Same rule: subtract the bottom exponent from the top exponent. Subtracting negative 1 adds 1 to the exponent.
5

Divide z terms using exponent rule

Subtract the bottom exponent from the top exponent. Negative 14 minus negative 8 equals negative 6.
6

Combine all terms into final answer

Put all three results together. We rewrite the negative exponent on z as a positive exponent in the denominator to keep the expression clean.

Understanding this problem

Learning Insight

The key rule here is . This works because dividing means canceling repeated factors, and subtraction of exponents tracks exactly how many factors remain. Negative exponents just mean the factor belongs in the denominator instead of the numerator.

Quick Tip

When you see a negative exponent in the denominator like on the bottom, it 'flips' to on the top. So dividing by is the same as multiplying by .

Common Mistake

Students often subtract exponents in the wrong order, computing bottom minus top instead of top minus bottom. Always do (numerator exponent) − (denominator exponent), not the reverse.