114 practice questions covering Power Play, organised into 2 topics.
114 questions include a written explanation.
Pick a topic below, or try the samples first.
An exponent of $1$ means the base appears exactly once as a factor, so $17^1 = 17$. The value $1$ mistakes the exponent for the answer, $171$ joins the digits, and $34$ doubles the base.
Q2
medium
Assertion (A): $(2^2)^3 = 2^6$. Reason (R): When a power is raised to another power, the exponents are multiplied.
ABoth A and R are true, and R is the correct explanation of A
BBoth A and R are true, but R is not the correct explanation of A
CA is true, but R is false
DA is false, but R is true
Show answer and explanation
Correct answer: A - Both A and R are true, and R is the correct explanation of A
A is true, since $(2^2)^3 = 4 \times 4 \times 4 = 64 = 2^6$. R states the rule correctly, and it is exactly why $2 \times 3 = 6$ appears as the exponent. So both are true and R explains A.
Q3
medium
Assertion (A): $5 \times 10^8$ is greater than $6 \times 10^7$. Reason (R): When two numbers are in standard form, the one with the bigger first number is always the greater.
ABoth A and R are true, and R is the correct explanation of A
BBoth A and R are true, but R is not the correct explanation of A
CA is true, but R is false
DA is false, but R is true
Show answer and explanation
Correct answer: C - A is true, but R is false
A is true, as $500000000$ beats $60000000$. R is false: this very pair has the smaller first number $5$ giving the larger value, because the power of ten is compared first. So a true assertion sits with a false reason.
Q4
easy
Which single power equals $(2^3)^2$?
A$2^5$
B$2^6$
C$2^9$
D$4^6$
Show answer and explanation
Correct answer: B - $2^6$
When a power is raised to another power the exponents multiply, so $3 \times 2 = 6$ gives $2^6$. Adding them gives $2^5$, raising to the wrong exponent gives $2^9$, and $4^6$ squares the base as well, which the rule does not do.
Q5
easy
Write $60000$ in standard form.
A$6 \times 10^4$
B$6 \times 10^5$
C$6 \times 10^2$
D$6 \times 10^3$
Show answer and explanation
Correct answer: A - $6 \times 10^4$
There are four zeros after the $6$, so the number is $6 \times 10^4$. The other choices give $600000$, $6000$ and $600$, each off by a power of ten.
Q6
easy
How is $9^2$ read aloud?
ANine squared
BNine cubed
CTwo squared
DNine times two
Show answer and explanation
Correct answer: A - Nine squared
A power with exponent $2$ is read as the base 'squared', so $9^2$ is 'nine squared' and equals $81$. 'Two squared' would be $2^2 = 4$, 'nine times two' is $18$, and 'nine cubed' is $9^3$.
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