Indices

[Admin]

#15117

Index Laws

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

$${x^a} \div {x^b} = {x^{a – b}}$$

$$\frac{{{x^a}}}{{{x^b}}} = {x^{a – b}}$$

$${\left( {{x^a}} \right)^b} = {x^{a \times b}}$$

$$x^{-1}=\frac{1}{x}$$

$$x^{-2}=\frac{1}{x^2}$$

a negative index means a fraction

$$x^{\frac12}=\sqrt{x}$$

$$x^{\frac13}=\sqrt[3]{x}$$

a fractional index means a root

[Admin]

#15120

Simplify $$\frac{{7{a^2}b^4}}{{3{a^6}{b^7}}} \div {\left( {\frac{{3ab}}{{2{a^6}{b^4}}}} \right)^3}$$

$$\frac{7}{{3{a^4}{b^3}}} \div \frac{{27{a^3}{b^3}}}{{8{a^{18}}{b^{12}}}}$$

$$ = \frac{7}{{3{a^4}{b^3}}} \times \frac{{8{a^{18}}{b^{12}}}}{{27{a^3}{b^3}}}$$

$$ = \frac{7}{{3{a^4}{b^3}}} \times \frac{{8{a^{15}}{b^9}}}{{27}}$$

$$=\frac{{56{a^{11}}{b^6}}}{{81}}$$

[Admin]

#15121

Simplify $${\left( {\frac{{2{m^3}{n^2}}}{{3m{n^5}}}} \right)^3} \times \frac{{6{m^2}{n^4}}}{{4{m^3}{n^{10}}}}$$

$$ = \frac{{8{m^9}{n^6}}}{{27{m^3}{n^{15}}}} \times \frac{{6{m^2}{n^4}}}{{4{m^3}{n^{10}}}}$$

$$ = \frac{{4{m^{11}}{n^{10}}}}{{9{m^6}{n^{25}}}}$$

$$ = \frac{{4{m^5}}}{{9{n^{15}}}}$$

[Admin]

#15122

Simplify $${\left( {\frac{{2{m^3}{n^2}}}{{3m{n^5}}}} \right)^3} \times \frac{{6{m^2}{n^4}}}{{4{m^3}{n^{10}}}}$$

$$ = \frac{{8{m^9}{n^6}}}{{27{m^3}{n^{15}}}} \times \frac{{6{m^2}{n^4}}}{{4{m^3}{n^{10}}}}$$

$$ = \frac{{4{m^{11}}{n^{10}}}}{{9{m^6}{n^{25}}}}$$

$$ = \frac{{4{m^5}}}{{9{n^{15}}}}$$

[Admin]

#18958

Evaluate 49½ + 50– 2-1,showing all steps of your working.
$$49^{\frac12}=\sqrt{49}$$ = 7	49 to the power of a half means the square root of 49 which is 7
$$5^0=1$$	anything to the power of zero is 1, so 5 to the power of zero is 1
$$2^{-1}-\frac12$$	2 to the power of negative 1 means 1 over 2 to the power of 1, which is the same as 1 over 2
$$49^{\frac12}+5^0-2^{-1}-\frac12$$ $$=\sqrt{49}+1-\frac12$$ =$$7\frac12$$

[Admin]

#18959

Simplify ##\frac{{6{x^{\frac{3}{2}}}{y^{\frac{1}{2}}} \times {x^{\frac{4}{5}y\frac{3}{5}}}}}{{2{{\left( {{x^{\frac{1}{2}}}y} \right)}^{\frac{1}{5}}} \times 3{x^{\frac{1}{2}}}{y^{\frac{1}{5}}}}}##

## = \frac{{6{x^{\frac{{23}}{{10}}}}{y^{\frac{{11}}{{10}}}}}}{{6{x^{\frac{1}{{10}}}}{y^{\frac{1}{5}}} \times {x^{\frac{1}{2}}}{y^{\frac{1}{5}}}}}##

## = \frac{{{x^{\frac{{23}}{{10}}}}{y^{\frac{{11}}{{10}}}}}}{{{x^{\frac{3}{5}}}{y^{\frac{2}{5}}}}}##

## = {x^{\frac{{17}}{{10}}}}{y^{\frac{7}{{10}}}}##

[Author]

Posts