Basic Math Examples

$2^{2 Z} = 2^{Z} \cdot \frac{2^{3 z}}{2}$

Step 1

Raise $2$ to the power of $1$ .

$2^{2 Z} = 2^{Z} \cdot \frac{2^{3 z}}{2^{1}}$

Step 2

Move $2^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$2^{2 Z} = 2^{Z} \cdot (2^{3 z} \cdot 2^{- 1})$

Step 3

Multiply $2^{Z}$ by $2^{3 z}$ by adding the exponents.

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Step 3.1

Move $2^{3 z}$ .

$2^{2 Z} = 2^{3 z} \cdot 2^{Z} \cdot 2^{- 1}$

Step 3.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2^{2 Z} = 2^{3 z + Z} \cdot 2^{- 1}$

Step 4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2^{2 Z} = 2^{3 z + Z - 1}$

Step 5

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$2 Z = 3 z + Z - 1$

Step 6

Move all terms containing $Z$ to the left side of the equation.

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Step 6.1

Subtract $Z$ from both sides of the equation.

$2 Z - Z = 3 z - 1$

Step 6.2

Subtract $Z$ from $2 Z$ .

$Z = 3 z - 1$