Question

Exponent Laws - difference between product law and product raised to a power (with formula please)

Answer 1

Answer:

Exponent laws:

1. Product law

$x^{a}\times x^{b}\times x^{c}=x^{a+b+c}$

In product law if bases are same then we add their respective powers.But if bases are different we can't add their powers.

x=base, a,b,c=exponent

If x=2 and a=3, b=5 , and c=10, then

$2^{3}\times2^{5}\times2^{10}=2^{3+5+10}=2^{18}$

2.Product raised to a power

1. $[x^{a}]^{c}=x^{ac}$

2. $[x^{a}\times x^{b}]^{c}=[x^{a+b}]^{c}=x^{ac+bc}$

If product is raised to a certain power , keeping the base same , we just multiply the powers.for example

$[2^{3}]^{4}=2^{3\times4}=2^{12}$ and

$[2^{3}\times3^{2}]^{2}=[2^{3}]^2 \times[3^{2}]^{2}=2^{6}\times3^{4}$

$[2^{3}\times2^{2}]^{2}=[2^{3+2}]^{2}=[2^{5}]^{2}=2^{10}$