**Introduction to exponents:**

In this article we discuss grade 7 math exponents solving problems. The exponents is the function e^{x}, where e is the number (approximately 2.718281828) such that the function e^{x} equals its own derivative. The exponential function is used to model phenomena when a constant change in the independent variable gives the same proportional change (increase or decrease) in the dependent variable. The exponents function is often written as exp(x), especially when the input is an expression too complex to be written as an exponents.( Source – Wikipedia)

The grade 7 math exponents solving problems are given below.

**Example 1:**

Multiply -6a^{2}bc, 2a^{2}b and` -1/4`

**Solution:**

We have learn that to find the product of three numbers, we first multiply two of them and then multiply the product obtained by the thirdnumber. Thus

= (-6a^{2}bc) (2a^{2}b) `(-1/4)`

= [(-6a^{2}bc) (2a^{2}b)] `(-1/4)`

= [(- 6x2) (a^{2} a^{2}) (b b) c] `(-1/4)`

= (-12a^{4} b^{2} c)` (-1/4) `

= [ (-12) `(-1/4)` ] a^{4} b^{2} c

= 3a^{4} b^{2} c

**Note:** 3 = -6 * 2 * `(-1/4)` and a^{4}b^{2}c = a^{2}bc * a^{2}b

(Since two negative number multiplied makes one affirmative or positive number)

**Example 2:**

Find the product of `(-3/2)` x^{2}, 6x y, 5xyz^{2} and -4 verify the result for x="1," y="2," z="0.5

**Solution:**

The product as [`-3/2` 6 (x^{2} x) y] [5 (-4) xyz^{2}]

= (-9x^{3}y) (-20xyz^{2})

= [ -9 (-20)] (x^{3 }x) (y y) z^{2}

= 180 x^{4 }* 6 * 5 * (-4) and x^{4}y^{2}z^{2} = xy xyz^{2}

= let us verify the product for x = 1, y = 2 and z = 0.5

LHS = [`-3/2` * 1^{2}] * (6 * 1 * 2) * [5 * 1 * 2 * (0.5)^{2}] * - 4

= `-3/2` * 12 * 2.5 * (-4)

= 180

RHS = 180(1)^{4 }(2)^{2 }(0.5)^{2}

= 180 4 0.25

=180

Thus, we observe that the coefficient of the product of two or more monomials is equal to the product of their coefficient and the variable part of the product is equal to the product of the variable in the givenmonomials.

**Example 3:**

Evaluate 102^{2}

**Solution:**

102^{2} = (100+2)^{2}

= 100^{2} + 2 * 100 * 2 +2^{2}

^{ }= 10000+400+4

= 10404

The solution is 10404.