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Popular >

simplify (510^6)(510^7)

Solution

simplify

(5 \cdot 1 0^{6}) (5 \cdot 1 0^{7})

Solution

5^{15} \cdot 8192

+1

Solution steps

(5 \cdot 1 0^{6}) (5 \cdot 1 0^{7})

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

1 0^{6} \cdot 1 0^{7} = 1 0^{6 + 7}

= 5 \cdot 5 \cdot 1 0^{6 + 7}

Add the numbers:

6 + 7 = 13

= 5 \cdot 5 \cdot 1 0^{13}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

5 \cdot 5 = 5^{1 + 1}

= 5^{1 + 1} \cdot 1 0^{13}

Add the numbers:

1 + 1 = 2

= 5^{2} \cdot 1 0^{13}

Factor integer

10 = 5 \cdot 2

= 5^{2} (5 \cdot 2)^{13}

Apply exponent rule:

(ab)^{c} = a^{c} b^{c}

(5 \cdot 2)^{13} = 5^{13} \cdot 2^{13}

= 5^{2} \cdot 5^{13} \cdot 2^{13}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

5^{2} \cdot 5^{13} = 5^{2 + 13}

= 5^{2 + 13} \cdot 2^{13}

Add the numbers:

2 + 13 = 15

= 5^{15} \cdot 2^{13}

2^{13} = 8192

= 5^{15} \cdot 8192

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Frequently Asked Questions (FAQ)

What is (5*10^6)(5*10^7) ?
The solution to (5*10^6)(5*10^7) is 5^{15}*8192