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Popular >

simplify (210^8)(210^6)

Solution

simplify

(2 \cdot 1 0^{8}) (2 \cdot 1 0^{6})

Solution

5^{14} \cdot 65536

+1

Decimal Notation

4.0 E 14

Solution steps

(2 \cdot 1 0^{8}) (2 \cdot 1 0^{6})

Apply exponent rule:

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

1 0^{8} \cdot 1 0^{6} = 1 0^{8 + 6}

= 2 \cdot 2 \cdot 1 0^{8 + 6}

Add the numbers:

8 + 6 = 14

= 2 \cdot 2 \cdot 1 0^{14}

Apply exponent rule:

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

2 \cdot 2 = 2^{1 + 1}

= 2^{1 + 1} \cdot 1 0^{14}

Add the numbers:

1 + 1 = 2

= 2^{2} \cdot 1 0^{14}

Factor integer

10 = 2 \cdot 5

= 2^{2} (2 \cdot 5)^{14}

Apply exponent rule:

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

(2 \cdot 5)^{14} = 2^{14} \cdot 5^{14}

= 2^{2} \cdot 2^{14} \cdot 5^{14}

Apply exponent rule:

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

2^{2} \cdot 2^{14} = 2^{2 + 14}

= 2^{2 + 14} \cdot 5^{14}

Add the numbers:

2 + 14 = 16

= 2^{16} \cdot 5^{14}

2^{16} = 65536

= 5^{14} \cdot 65536

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Frequently Asked Questions (FAQ)

What is (2*10^8)(2*10^6) ?
The solution to (2*10^8)(2*10^6) is 5^{14}*65536