What is ((7^5)^8*7^7)/(7^8*(7^8)^5) ?

The solution to ((7^5)^8*7^7)/(7^8*(7^8)^5) is 1/7

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simplify ((7^5)^87^7)/(7^8(7^8)^5)

simplify

\frac{( 7 ^{5} ) ^{8} \cdot 7 ^{7}}{7 ^{8} \cdot ( 7 ^{8} ) ^{5}}

\frac{1}{7}

Decimal Notation

0.14285 \dots

Solution steps

\frac{( 7 ^{5} ) ^{8} \cdot 7 ^{7}}{7 ^{8} ( 7 ^{8} ) ^{5}}

\frac{( 7 ^{5} ) ^{8} \cdot 7 ^{7}}{7 ^{8} ( 7 ^{8} ) ^{5}} = \frac{7 ^{40} \cdot 7 ^{7}}{7 ^{8} \cdot 7 ^{40}}

= \frac{7 ^{40} \cdot 7 ^{7}}{7 ^{8} \cdot 7 ^{40}}

Cancel the common factor:

7^{40}

= \frac{7 ^{7}}{7 ^{8}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

= \frac{1}{7 ^{8 - 7}}

Subtract the numbers:

8 - 7 = 1

= \frac{1}{7 ^{1}}

Apply exponent rule:

a^{1} = a

7^{1} = 7

= \frac{1}{7}

\frac{5}{6} + \frac{2}{5}

\frac{sin ( 3 x )}{cos ( 3 x )}

\frac{7}{8} - \frac{3}{5}

(\frac{2}{3})^{2} (\frac{2}{3})^{3}

x^{3} - 3^{3}

What is ((7^5)^8*7^7)/(7^8*(7^8)^5) ?
The solution to ((7^5)^8*7^7)/(7^8*(7^8)^5) is 1/7