Basic Math Examples

$3^{\sqrt{54 y^{4}}} - y^{3 \sqrt{16 y}}$

Step 1

Rewrite $54 y^{4}$ as ${(3 y^{2})}^{2} \cdot 6$ .

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Step 1.1

Factor $9$ out of $54$ .

$3^{\sqrt{9 (6) y^{4}}} - y^{3 \sqrt{16 y}}$

Step 1.2

Rewrite $9$ as $3^{2}$ .

$3^{\sqrt{3^{2} \cdot 6 y^{4}}} - y^{3 \sqrt{16 y}}$

Step 1.3

Rewrite $y^{4}$ as ${(y^{2})}^{2}$ .

$3^{\sqrt{3^{2} \cdot 6 {(y^{2})}^{2}}} - y^{3 \sqrt{16 y}}$

Step 1.4

Move $6$ .

$3^{\sqrt{3^{2} {(y^{2})}^{2} \cdot 6}} - y^{3 \sqrt{16 y}}$

Step 1.5

Rewrite $3^{2} {(y^{2})}^{2}$ as ${(3 y^{2})}^{2}$ .

$3^{\sqrt{{(3 y^{2})}^{2} \cdot 6}} - y^{3 \sqrt{16 y}}$

Step 2

Pull terms out from under the radical.

$3^{3 y^{2} \sqrt{6}} - y^{3 \sqrt{16 y}}$

Step 3

Rewrite $16 y$ as ${(2^{2})}^{2} y$ .

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Step 3.1

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

$3^{3 y^{2} \sqrt{6}} - y^{3 \sqrt{4^{2} y}}$

Step 3.2

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

$3^{3 y^{2} \sqrt{6}} - y^{3 \sqrt{{(2^{2})}^{2} y}}$

Step 4

Pull terms out from under the radical.

$3^{3 y^{2} \sqrt{6}} - y^{3 (2^{2} \sqrt{y})}$

Step 5

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

$3^{3 y^{2} \sqrt{6}} - y^{3 (4 \sqrt{y})}$

Step 6

Multiply $4$ by $3$ .

$3^{3 y^{2} \sqrt{6}} - y^{12 \sqrt{y}}$