Algebra Examples

$0.9 = 2 {(\frac{2 h}{32})}^{\frac{1}{2}}$

Step 1

Rewrite the equation as $2 {(\frac{2 h}{32})}^{\frac{1}{2}} = 0.9$ .

$2 {(\frac{2 h}{32})}^{\frac{1}{2}} = 0.9$

Step 2

Reduce the expression $\frac{2 h}{32}$ by cancelling the common factors.

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Step 2.1

Factor $2$ out of $2 h$ .

$2 {(\frac{2 (h)}{32})}^{\frac{1}{2}} = 0.9$

Step 2.2

Factor $2$ out of $32$ .

$2 {(\frac{2 h}{2 \cdot 16})}^{\frac{1}{2}} = 0.9$

Step 2.3

Cancel the common factor.

$2 {(\frac{2 h}{2 \cdot 16})}^{\frac{1}{2}} = 0.9$

Step 2.4

Rewrite the expression.

$2 {(\frac{h}{16})}^{\frac{1}{2}} = 0.9$

Step 3

Divide each term in $2 {(\frac{h}{16})}^{\frac{1}{2}} = 0.9$ by $2$ and simplify.

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Step 3.1

Divide each term in $2 {(\frac{h}{16})}^{\frac{1}{2}} = 0.9$ by $2$ .

$\frac{2 {(\frac{h}{16})}^{\frac{1}{2}}}{2} = \frac{0.9}{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Reduce the expression by cancelling the common factors.

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Step 3.2.1.1

Cancel the common factor.

$\frac{2 {(\frac{h}{16})}^{\frac{1}{2}}}{2} = \frac{0.9}{2}$

Step 3.2.1.2

Simplify the expression.

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Step 3.2.1.2.1

Divide ${(\frac{h}{16})}^{\frac{1}{2}}$ by $1$ .

${(\frac{h}{16})}^{\frac{1}{2}} = \frac{0.9}{2}$

Step 3.2.1.2.2

Apply the product rule to $\frac{h}{16}$ .

$\frac{h^{\frac{1}{2}}}{16^{\frac{1}{2}}} = \frac{0.9}{2}$

Step 3.2.2

Simplify the denominator.

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Step 3.2.2.1

Rewrite $16$ as $4^{2}$ .

$\frac{h^{\frac{1}{2}}}{{(4^{2})}^{\frac{1}{2}}} = \frac{0.9}{2}$

Step 3.2.2.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{h^{\frac{1}{2}}}{4^{2 (\frac{1}{2})}} = \frac{0.9}{2}$

Step 3.2.2.3

Cancel the common factor of $2$ .

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Step 3.2.2.3.1

Cancel the common factor.

$\frac{h^{\frac{1}{2}}}{4^{2 (\frac{1}{2})}} = \frac{0.9}{2}$

Step 3.2.2.3.2

Rewrite the expression.

$\frac{h^{\frac{1}{2}}}{4^{1}} = \frac{0.9}{2}$

Step 3.2.2.4

Evaluate the exponent.

$\frac{h^{\frac{1}{2}}}{4} = \frac{0.9}{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $0.9$ by $2$ .

$\frac{h^{\frac{1}{2}}}{4} = 0.45$

Step 4

Multiply both sides of the equation by $4$ .

$4 \frac{h^{\frac{1}{2}}}{4} = 4 \cdot 0.45$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $4$ .

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Step 5.1.1.1

Cancel the common factor.

$4 \frac{h^{\frac{1}{2}}}{4} = 4 \cdot 0.45$

Step 5.1.1.2

Rewrite the expression.

$h^{\frac{1}{2}} = 4 \cdot 0.45$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $4$ by $0.45$ .

$h^{\frac{1}{2}} = 1.8$

Step 6

Raise each side of the equation to the power of $2$ to eliminate the fractional exponent on the left side.

${(h^{\frac{1}{2}})}^{2} = {1.8}^{2}$

Step 7

Simplify the exponent.

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Step 7.1

Simplify the left side.

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Step 7.1.1

Simplify ${(h^{\frac{1}{2}})}^{2}$ .

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Step 7.1.1.1

Multiply the exponents in ${(h^{\frac{1}{2}})}^{2}$ .

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Step 7.1.1.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$h^{\frac{1}{2} \cdot 2} = {1.8}^{2}$

Step 7.1.1.1.2

Cancel the common factor of $2$ .

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Step 7.1.1.1.2.1

Cancel the common factor.

$h^{\frac{1}{2} \cdot 2} = {1.8}^{2}$

Step 7.1.1.1.2.2

Rewrite the expression.

$h^{1} = {1.8}^{2}$

Step 7.1.1.2

Simplify.

$h = {1.8}^{2}$

Step 7.2

Simplify the right side.

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Step 7.2.1

Raise $1.8$ to the power of $2$ .

$h = 3.24$