EXPONENT PROPERTIES AND SCIENTIFIC NOTATION WORKSHEET

About "Exponent properties and scientific notation worksheet"

Exponent properties and scientific notation worksheet :

Here we are going to see some practice questions on exponent properties and scientific notation.

Question 1 :

Simplify the following expression

Solution :

= (2x⁵)⁴ (x³)²

By distributing the power, we get

= 2⁴(x⁵)⁴ (x³)²

= 16 x²⁰ x⁶

Since we have same base, we need to write only one base and combine the powers according to their signs.

= 16 x^{(20 + 6)}

= 16 x²⁶

Question 2 :

Simplify the following expression

Solution :

= (2x^-3)³ (3x³)²

By distributing the power, we get

= 2³(x^-3)³ 3²(x³)²

= 8x^-9 ⋅ 9x⁶

= 8⋅ 9x^{(-9 + 6)}

= 72x^-3

= 72/x³

Question 3 :

Simplify the following expression

Solution :

= (2x³)² (a⁰)⁵

By distributing the power, we get

= 2²(x³)² (1)⁵

= 4 x⁶ (1)

= 4 x⁶

Question 4 :

Simplify the following expression

Solution :

= (3x⁶/2y⁹) ⋅ (y⁵/x³)

Here we need to combine the x and y terms.Let us combine the x terms in the numerator and y terms in the denominator.

= (3x⁶⋅x³⁾/(2y⁹⋅ y⁵)

= 3x^{(6 + 3)}/2y^{(9 + 5)}

= 3x⁹/2y¹⁴

Question 5 :

Simplify the following expression

Solution :

= (2x²y^-3) (3x^-4y^-2)

= 2⋅3 x^(2-4)y^{(-3 - 2)}

= 6 x^-2y^-5

= 6/x²y⁵

Question 6 :

Archimedes estimated the universe to be 2.3 x 10¹⁹ millimeters (mm) in diameter. If this number were written in standard or decimal form, how many 0s would follow the digit 3?

Solution :

To write 2.3 x 10¹⁹ in standard form, we have to move the decimal point 19 digits. Since we have only one number after the decimal point we have to write 18 zeroes.

2.3 x 10¹⁹ = 23000000000000000000

Question 7 :

perform the indicated calculations. Write your result in scientific notation.

(2 x 10⁵ )(4 x 10⁴ )

Solution :

= (2 x 10⁵ )(4 x 10⁴ )

= 2 x 4 x 10⁵ x 10⁴

= 8 x 10^{(5 + 4)}

= 8 x 10⁹

Question 7 :

Can (a + b)^-1 be written as (1/a) + (1/b) by using the properties of exponents? If not, why not? Explain.

Solution :

In order to convert the power as positive, we need to write its reciprocal.

That is,

(a + b)^-1 = 1/(a + b)

But 1/(a + b) is not equal to (1/a) + (1/b)

Question 7 :

If n > 0, which of the following expressions are negative? -n^-3 , n^-3 , (-n)^-3 , (-n)³ , -n³

Solution :

n > 0 means, n is a positive

(i) -n^-3 = 1/-n³ ==> -1/n³(Negative)

Though we have changed it as positive exponent, it is negative

(ii) n^-3 = 1/n³ ==> 1/n³(Positive)

(iii) (-n)^-3 = 1/(-n)³ = 1/(-n³)= -1/n³(Negative)

(iv) (-n)³

By distributing the power, we get

= -n³ (Negative)

(v) -n³ (Negative)

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