What is (45^{45}*15^{15})/(75^{30)} ?

The solution to (45^{45}*15^{15})/(75^{30)} is 3^{75}

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simplify (45^{45}*15^{15})/(75^{30)}

simplify

\frac{4 5 ^{45} \cdot 1 5 ^{15}}{7 5 ^{30}}

3^{75}

Solution steps

\frac{4 5 ^{45} \cdot 1 5 ^{15}}{7 5 ^{30}}

Factor

4 5^{45} : 1 5^{45} \cdot 3^{45}

= \frac{1 5 ^{45} \cdot 3 ^{45} \cdot 1 5 ^{15}}{7 5 ^{30}}

Factor

7 5^{30} : 1 5^{30} \cdot 5^{30}

= \frac{1 5 ^{45} \cdot 3 ^{45} \cdot 1 5 ^{15}}{1 5 ^{30} \cdot 5 ^{30}}

\frac{1 5 ^{45}}{1 5 ^{30}} = 1 5^{15}

= \frac{1 5 ^{15} \cdot 3 ^{45} \cdot 1 5 ^{15}}{5 ^{30}}

Factor

1 5^{15} : 5^{15} \cdot 3^{15}

= \frac{5 ^{15} \cdot 3 ^{15} \cdot 3 ^{45} \cdot 1 5 ^{15}}{5 ^{30}}

\frac{5 ^{15}}{5 ^{30}} = \frac{1}{5 ^{15}}

= \frac{3 ^{15} \cdot 3 ^{45} \cdot 1 5 ^{15}}{5 ^{15}}

Factor

1 5^{15} : 5^{15} \cdot 3^{15}

= \frac{3 ^{15} \cdot 3 ^{45} \cdot 5 ^{15} \cdot 3 ^{15}}{5 ^{15}}

Cancel the common factor:

5^{15}

= 3^{15} \cdot 3^{45} \cdot 3^{15}

3^{15} \cdot 3^{45} \cdot 3^{15} = 3^{75}

= 3^{75}

∣ x - 4 ∣ + 7 = 8

64 x^{2} - 121

x^{2} - 8 x = 16

y^{2} - 5 y + 2 = 0

32 = y - 8 - 13 y

What is (45^{45}*15^{15})/(75^{30)} ?
The solution to (45^{45}*15^{15})/(75^{30)} is 3^{75}