ANSWER
a. 16
b. 1
c. 64
d. 64
EXPLANATION
We want to simplify the following exponential expressions
a.
[tex] {2}^{4} [/tex]
This implies that
[tex] {2}^{4} = 2 \times 2 \times 2 \times 2[/tex]
[tex] {2}^{4} = 16[/tex]
b. Any non-zero number exponent zero is 1.
This implies that,
[tex] {3}^{0} = 1[/tex]
c. The given exponentiial expression is,
[tex] {4}^{6} \times {4}^{ - 3} [/tex]
The bases are the same so we add the exponents.
[tex] {4}^{6} \times {4}^{ - 3} = {4}^{6 + - 3} [/tex]
This simplifies to,
[tex]{4}^{6} \times {4}^{ - 3} = {4}^{3} [/tex]
[tex]{4}^{6} \times {4}^{ - 3} = 4 \times 4 \times 4 = 64[/tex]
d. We want to simplify:
[tex] { ({2}^{3}) }^{2} [/tex]
This is the same as
[tex]{ ({2}^{3}) }{ ({2}^{3}) }[/tex]
We add the exponents now to get:
[tex]{2}^{3 + 3} = {2}^{6} = 64[/tex]
