How do you use the laws of exponents to simplify the expression $b^{8} {(2 b)}^{4}$ $b^8(2b)^4$ ?

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Answer 1 · 2015-05-19T15:03:23

One law of the exponents states that ${(a^{n})}^{m} = a^{n} \cdot m$ $(a^n)^m=a^n*m$

Then,

$b^{8} {(2^{1} b^{1})}^{4} = b^{8} (2^{1 \cdot 4} b^{1 \cdot 4})$ $b^8(2^1b^1)^4=b^8(2^(1*4)b^(1*4))$

Now, we get $b^{8} (16 b^{4}) = 16 \cdot b^{8} \cdot b^{4}$ $b^8(16b^4)=16*b^8*b^4$ .

Another law of exponents states that $a^{n} \cdot a^{m} = a^{n + m}$ $a^n*a^m=a^(n+m)$ . Thus,

$16 \cdot b^{8 + 4} = 16 b^{12}$ $16*b^(8+4)=16b^12$

How do you use the laws of exponents to simplify the expression b8(2b)4b^8(2b)^4?