5) Which is equivalent to the expression shown? 5^-3
a. -125
b. -15 ****
c. 1/125
d. 2
6) Which is equivalent to the expression shown? 10^2 . 5^2
a. 2,500 *******
b. 250
c. 500
d. 200
7) The value of Square root 60 is between which pair of consecutive numbers?
a. 59 and 60
b. 7 and 8 ****
c. 8 and 9
d. 9 and 10
Online, “*” is used to indicate multiplication to avoid confusion with “x” as an unknown.
5. wrong, 5^-3 = 1/5^3
6 & 7 are right.
how can I make equivalent powers:
2 ----- 6 x 10^-9
5) The answer is (c) 1/125.
To solve this problem, we need to remember that 5^-3 is equivalent to 1/5^3.
So, 5^-3 = 1/5^3 = 1/(5 * 5 * 5) = 1/125.
6) The answer is (a) 2,500.
To solve this problem, we need to remember that when we multiply two powers with the same base, we add their exponents.
So, 10^2 . 5^2 = (10 * 10) . (5 * 5) = 100 . 25 = 2,500.
7) The answer is (b) 7 and 8.
To find the pair of consecutive numbers between which the square root of 60 lies, we can estimate the square root.
The square root of 60 is approximately 7.745966692414834.
Therefore, the square root of 60 lies between 7 and 8.
To answer these questions, we need to understand the concepts of exponents and square roots.
5) The expression 5^-3 means taking the reciprocal of 5 cubed (5^3). To evaluate this, we can rewrite it as 1/(5^3). Therefore, we calculate 5^3 = 5 * 5 * 5 = 125. Taking the reciprocal gives us 1/125.
6) The expression 10^2 * 5^2 means multiplying 10 squared (10^2) by 5 squared (5^2). To evaluate this, we need to calculate 10^2 = 10 * 10 = 100 and 5^2 = 5 * 5 = 25. Multiplying these together gives us 100 * 25 = 2,500.
7) The square root of 60 is a value that, when squared, equals 60. To find the approximate range of this value, we can look for the two consecutive square numbers around 60. The closest square numbers are 49 (7^2) and 64 (8^2). Therefore, the value of the square root of 60 lies between 7 and 8.
So the answers are:
5) c. 1/125
6) a. 2,500
7) b. 7 and 8