What is 5^9x3^9x15^{-7} ?

The solution to 5^9x3^9x15^{-7} is 225x^2

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simplify 5^9x3^9x15^{-7}

simplify

5^{9} x 3^{9} x 1 5^{- 7}

225 x^{2}

Solution steps

5^{9} x \cdot 3^{9} x \cdot 1 5^{- 7}

Apply exponent rule:

aa = a^{2}

xx = x^{2}

= 5^{9} x^{2} \cdot 3^{9} \cdot 1 5^{- 7}

= 5^{9} \cdot 3^{9} \cdot 1 5^{- 7} x^{2}

3^{9} = 19683

= 5^{9} \cdot 19683 \cdot 1 5^{- 7} x^{2}

1 5^{- 7} = \frac{1}{170859375}

= 5^{9} \cdot 19683 \cdot \frac{1}{170859375} x^{2}

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{5 ^{9} \cdot 19683 \cdot 1 \cdot x ^{2}}{170859375}

Multiply the numbers:

19683 \cdot 1 = 19683

= \frac{5 ^{9} \cdot 19683 x ^{2}}{170859375}

Factor the number:

19683 = 2187 \cdot 9

= \frac{5 ^{9} \cdot 2187 \cdot 9 x ^{2}}{170859375}

Factor the number:

170859375 = 2187 \cdot 78125

= \frac{5 ^{9} \cdot 2187 \cdot 9 x ^{2}}{2187 \cdot 78125}

Cancel the common factor:

2187

= \frac{5 ^{9} \cdot 9 x ^{2}}{78125}

Factor the number:

78125 = 5^{7}

= \frac{5 ^{9} \cdot 9 x ^{2}}{5 ^{7}}

\frac{5 ^{9}}{5 ^{7}} = 5^{2}

= 5^{2} \cdot 9 x^{2}

5^{2} = 25

= 25 \cdot 9 x^{2}

Multiply the numbers:

25 \cdot 9 = 225

= 225 x^{2}

e^{- 0.0639}

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