Frankly, the red part does not make any sense...

The denominator is \(2^7*5^7\). Multiply it by \(2^4\). What do you get?[/quote]

Hello Bunuel, i have the same question: based on which rule are you multiplying (2^3*5^7) by 2^4 but still ignoring 5^7 ? please help me to understand your smart solution and to answer your question: if multiply (2^3*5^7) by 2^4 I get 2^7 *10^11 Thanks![/quote]

Hi dave13

Properties of exponents say that if base is equal then on multiplying you add the powers and on dividing you subtract the powers

i.e. \(a^b*c^d\) if multiplied by \(a^x\), then it will become \(a^{(b+x)}*c^d\), here there will be no impact on \(c^d\) which has a different base.

In this problem as \(5^7\) has a power of \(7\) so we need to make \(2^3\) as \(2^7\), hence we multiply the numerator & denominator by \(2^4\)

so \(2^3*5^7*2^4=2^{(3+4)}*5^7=2^7*5^7=(2*5)^7=10^7\)

Hello Bunuel, i have the same question: based on which rule are you multiplying (2^3*5^7) by 2^4 but still ignoring 5^7 ? please help me to understand your smart solution and to answer your question: if multiply (2^3*5^7) by 2^4 I get 2^7 *10^11 Thanks![/quote]

Hi dave13

Properties of exponents say that if base is equal then on multiplying you add the powers and on dividing you subtract the powers

i.e. \(a^b*c^d\) if multiplied by \(a^x\), then it will become \(a^{(b+x)}*c^d\), here there will be no impact on \(c^d\) which has a different base.

In this problem as \(5^7\) has a power of \(7\) so we need to make \(2^3\) as \(2^7\), hence we multiply the numerator & denominator by \(2^4\)

so \(2^3*5^7*2^4=2^{(3+4)}*5^7=2^7*5^7=(2*5)^7=10^7\)[/quote]

Thanks a lot niks18 for a detailed explanation. Highly appreciated!