Grade9 rational arithmetic and integer exponent laws
Preserve signs and the structure of an expression
Rational arithmetic requires attention to grouping and the order of operations. Parentheses determine which quantity is raised to a power or multiplied. Compare(-3)^4 with−3^4: the first has a negative base inside parentheses and equals 81, while the second commonly means the negative of 3^4 and equals−81. Do not assign a sign by looking at the last written number alone.
For fraction operations, use common denominators when adding or subtracting and multiply by the divisor's reciprocal when dividing by a nonzero fraction. A fraction can represent a negative number without changing the basic equality rules. Convert decimals or mixed numbers where that makes structure clearer, then check the approximate magnitude of the result.
Apply exponent laws with their conditions
For a common nonzero base, multiplying powers adds exponents and dividing powers subtracts them. Raising a power to an integer power multiplies the exponents. The rule concerns exponents, not addition of the original bases. For example,2^3×2^5=2^8, whereas 2^3+2^5 must be evaluated as a sum rather than rewritten with the same rule.
An exponent of zero gives one for a nonzero base. A negative integer exponent expresses a reciprocal, not a negative result:2^(−3)=1/8. Check that denominators and bases used in reciprocal operations are nonzero. These statements do not give permission to ignore domain restrictions or apply every rule unchanged to an undefined expression.
Use structure to reduce errors
In the supplied expression[(-2)^3×(-2)^4]/(-2)^5, the common base and grouping allow exponent arithmetic:3+4−5=2. The result is(-2)^2=4. Multiplying every factor separately gives the same value and can serve as a check.
Scientific notation combines a coefficient with a power of ten. Keep the coefficient and exponent roles distinct and verify that moving a decimal point has been balanced by the appropriate change in power. When approximating a quantity, report only the precision justified by the task and do not confuse an estimate with an exact equality.
These common mathematical foundations support the selected Saskatchewan number topics without certifying current assessment logistics or exact official weighting.