# Grade 9 Math: Linear Relations and Equations Product Rule for Exponents

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### What are the two conditions of the Product Rule?

The powers have to be multiplied together. The bases of the powers have to be the same.
The powers have to be divided together. The bases of the powers have to be the same.
The powers have to be multiplied together. The bases of the powers have to be difference.
The powers have to be added together. The bases of the powers have to be the same.

### Solving the following equation using the product rule: $$5^5+5^7$$

$$5^{12}$$
$$5^{35}$$
$$5^2$$
none of the above

### Solve the following equation: $$x^{3}\times y \times y\times x^{4} \times y^{3}$$

$$x^{2}y^{4}$$
$$x^{7}y^{5}$$
$$x^{7}y^{2}$$
$$x^{2}y^{4}$$

### Solving the following equation using the product rule: $$3^5\times3^2+3^7\times3^3\times3^3$$

$$3^2+3^{10}$$
$$3^6+3^{12}$$
$$3^6+3^{13}$$
$$3^7+3^{13}$$
### Solving the following equation using the product rule: $$2^3+2^7\times2^5+2^6\times2^3\times2^3+2^4\times3^6$$
$$2^3+2^{10}+2^{12}\times3^6$$
$$2^3+2^{12}+2^{12}\times3^6$$
$$2^3+2^{24}\times3^6$$
$$2^3+2^{24}\times3^2$$