Basic Math Examples

$1200 = 150 \cdot 2^{a + 4}$

Step 1

Rewrite the equation as $150 \cdot 2^{a + 4} = 1200$ .

$150 \cdot 2^{a + 4} = 1200$

Step 2

Divide each term in $150 \cdot 2^{a + 4} = 1200$ by $150$ and simplify.

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Step 2.1

Divide each term in $150 \cdot 2^{a + 4} = 1200$ by $150$ .

$\frac{150 \cdot 2^{a + 4}}{150} = \frac{1200}{150}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $150$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{150 \cdot 2^{a + 4}}{150} = \frac{1200}{150}$

Step 2.2.1.2

Divide $2^{a + 4}$ by $1$ .

$2^{a + 4} = \frac{1200}{150}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $1200$ by $150$ .

$2^{a + 4} = 8$

Step 3

Create equivalent expressions in the equation that all have equal bases.

$2^{a + 4} = 2^{3}$

Step 4

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

$a + 4 = 3$

Step 5

Move all terms not containing $a$ to the right side of the equation.

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Step 5.1

Subtract $4$ from both sides of the equation.

$a = 3 - 4$

Step 5.2

Subtract $4$ from $3$ .

$a = - 1$