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**Section - 1Simplify the following expressions by combining like terms. If the base is a number, leave the answer in exponential form (i.e. 23, not 8).**

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Ques 11: 3

= 3

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= y

= y

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(A) (-3)

(A) (-3)

(B) -3

The exponent is done before multiplication (by -1) because of the order of operations.

The value of this expression is positive.

-2 7 has the lowest value of the three answer choices that result in negative numbers. The correct answer is (B).

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The first two terms in the expression are in fact the same. Because these terms are equal, when the second is subtracted from the first they cancel out leaving only the third term.

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The correct answer is (E).

Note: when a problem asks you to find a different or more simplified version of the same thing, check your work against the answer choices frequently to ensure that you donâ€™t simplify or manipulate too far.

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Dividing a smaller positive number by a larger positive number will result in a number less than 1.

Dividing a larger positive number by a smaller positive number will result in a number greater than 1.

This answer is negative; therefore, it is less than 1.

Dividing a larger positive number by a smaller positive number will result in a number greater than 1.

(E) (-4)

This answer is negative; therefore, it is less than 1.

Simplify the following expressions by finding common bases.

**Ques 26: 8 ^{3} x 2^{6}**

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Simplify the following expressions by pulling out as many common factors as possible.

**Ques 31: 6 ^{3} + 3^{3} = (A) 3^{5} (B) 3^{9} (C) 2(3^{3})**Begin by breaking 6 down into its prime factors.

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6

(2 x 3)

(2

Now each term contains (3

(2

3

3

3

We have a match. The answer is A.

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81

(3

3

3

3

We have a match. The answer is B.

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15

(3 x 5)

(3

Now both terms contain 5

(3

5

5

5

We still donâ€™t have a match, but we can break 8 down into its prime factors.

5

5

We have a match. The answer is B.

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**Ques 40: Ans:**

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** ****Ques 42: ****Ans: ****Section - 7****Simplify the following roots. Not every answer will be an integer.****Ques 43: âˆš32****Ans: ****Ques 44: âˆš24****Ans: ****Ques 45: âˆš180****Ans:****Ques 46: âˆš490****Ans:****Ques 47: âˆš450****Ans:****Ques 48: âˆš135****Ans:****Ques 49: âˆš224****Ans: ****Ques 50: âˆš343****Ans: ****Section - 8****Simplify the following roots. You will be able to completely eliminate the root in every question. Ex- press answers as integers.****Ques 51: ****Ans: **Pull out the greatest common factor of 36^{2} and 15^{2}, namely 3^{2}, to give

Both 3^{2} and 169 are perfect squares (169 = 13^{2}), so**Ques 52: ****Ans:** Pull out the greatest common factor of 35^{2} and 21^{2}, namely 7^{2}, to give

Both 7^{2} and 16 are perfect squares (16 = 4^{2}), so**Ques 53: ****Ans: **Pull out the greatest common factor of 5^{6} and 5^{7}, namely 5^{6}, to give

Both 6^{2} and 5^{6 }are perfect squares (5^{6}= 5^{3 }x 5^{3}), so**Ques 54: ****Ans: **Pull out the greatest common factor of 8^{4} and 8^{5}, namely 8^{4}, to give

Both 8^{4} and 3^{2} are perfect squares (8^{4} = 8^{2} x 8^{2}), so**Ques 55: ****Ans: **Pull out the greatest common factor of 2^{15}, 2^{13}, and 2^{12}, namely 2^{12}, to give

Both 2^{12} and 3^{2} are perfect squares

(2^{12} = 2^{6} x 2^{6}), **Ques 56: ****Ans: **Pull out the greatest common factor of 50^{3} and 50^{2}, namely 50^{2}, to give

Both 50^{2} and 7^{2} are perfect squares, so

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