Question

Fully simplify (x8⋅x7)6(x2⋅x4)3\frac{\left(x^{8}\cdot x^{7}\right)^{6}}{\left(x^{2}\cdot x^{4}\right)^{3}}
(x
2
⋅x
4
)
3

(x
8
⋅x
7
)
6

​
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Answer 1

To simplify the expression \(\frac{(x^{8} \cdot x^{7})^{6}}{(x^{2} \cdot x^{4})^{3}}\), we can follow these steps:

1. **Simplify the numerators and denominators separately.**

First, let's simplify the numerator:
\[
(x^{8} \cdot x^{7})^{6} = (x^{8+7})^{6} = (x^{15})^{6} = x^{15 \cdot 6} = x^{90}.
\]

Now, let's simplify the denominator:
\[
(x^{2} \cdot x^{4})^{3} = (x^{2+4})^{3} = (x^{6})^{3} = x^{6 \cdot 3} = x^{18}.
\]

2. **Put the simplified numerator and denominator together.**

Now, we have:
\[
\frac{x^{90}}{x^{18}}.
\]

3. **Use the property of exponents.**

When dividing exponents with the same base, subtract the exponents:
\[
\frac{x^{90}}{x^{18}} = x^{90 - 18} = x^{72}.
\]

Thus, the fully simplified expression is:
\[
\boxed{x^{72}}.
\]