evaluatee thiis question
Answers
1 Remove parentheses.
\frac{{8}^{-3}\times {5}^{3}}{{2}^{-4}}
2
−4
8
−3
×5
3
2 Use Negative Power Rule: {x}^{-a}=\frac{1}{{x}^{a}}x
−a
=
x
a
1
.
\frac{\frac{1}{{8}^{3}}\times {5}^{3}}{{2}^{-4}}
2
−4
8
3
1
×5
3
3 Simplify {8}^{3}8
3
to 512512.
\frac{\frac{1}{512}\times {5}^{3}}{{2}^{-4}}
2
−4
512
1
×5
3
4 Simplify {5}^{3}5
3
to 125125.
\frac{\frac{1}{512}\times 125}{{2}^{-4}}
2
−4
512
1
×125
5 Simplify \frac{1}{512}\times 125
512
1
×125 to \frac{125}{512}
512
125
.
\frac{\frac{125}{512}}{{2}^{-4}}
2
−4
512
125
6 Use Negative Power Rule: {x}^{-a}=\frac{1}{{x}^{a}}x
−a
=
x
a
1
.
\frac{\frac{125}{512}}{\frac{1}{{2}^{4}}}
2
4
1
512
125
7 Simplify {2}^{4}2
4
to 1616.
\frac{\frac{125}{512}}{\frac{1}{16}}
16
1
512
125
8 Invert and multiply.
\frac{125}{512}\times 16
512
125
×16
9 Use this rule: \frac{a}{b} \times c=\frac{ac}{b}
b
a
×c=
b
ac
.
\frac{125\times 16}{512}
512
125×16
10 Simplify 125\times 16125×16 to 20002000.
\frac{2000}{512}
512
2000
11 Simplify.
\frac{125}{32}
32
125
Done
Remove parentheses.
{5}^{-1}\times {2}^{-1}\times {6}^{2}
5
−1
×2
−1
×6
2
2 Use Negative Power Rule: {x}^{-a}=\frac{1}{{x}^{a}}x
−a
=
x
a
1
.
\frac{1}{5}\times {2}^{-1}\times {6}^{2}
5
1
×2
−1
×6
2
3 Use Negative Power Rule: {x}^{-a}=\frac{1}{{x}^{a}}x
−a
=
x
a
1
.
\frac{1}{5}\times \frac{1}{2}\times {6}^{2}
5
1
×
2
1
×6
2
4 Simplify {6}^{2}6
2
to 3636.
\frac{1}{5}\times \frac{1}{2}\times 36
5
1
×
2
1
×36
5 Use this rule: \frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}
b
a
×
d
c
=
bd
ac
.
\frac{1\times 1\times 36}{5\times 2}
5×2
1×1×36
6 Simplify 1\times 11×1 to 11.
\frac{1\times 36}{5\times 2}
5×2
1×36
7 Simplify 1\times 361×36 to 3636.
\frac{36}{5\times 2}
5×2
36
8 Simplify 5\times 25×2 to 1010.
\frac{36}{10}
10
36
9 Simplify.
\frac{18}{5}
5
18
Done